Study of equilibrium, kinetic and thermodynamic parameters about methylene blue adsorption onto natural zeolite

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Abstract

Adsorption equilibrium and kinetic of methylene blue (MB) onto natural zeolite was studied in a batch system. Variables of the system include contact time, pH, salt concentration, temperature, and initial MB concentration. The increase in temperature resulted in a higher MB loading per unit weight of the zeolite. Langmuir, Freundlich, Redlich–Peterson, Koble–Corrigan and Temkin isotherm models were applied to experimental equilibrium data of MB adsorption depending on temperature. The effect of contact time at different temperatures and initial concentration were fitted to pseudo-second-order kinetic model. Linear regressive method and nonlinear regressive method were used to obtain the relative parameters. The error analysis was conducted to find whether linear method or nonlinear method was better to predict the experimental results and which model was better to fit the experimental data. Both methods were suitable to obtain the parameters. The Redlich–Peterson equation was best to fit the equilibrium data. The pseudo-second-order kinetic model can be used to describe the adsorption behavior. The nonlinear method may be better with the absolute error as limited condition. The adsorption process was spontaneous and endothermic.

Introduction

Adsorption has been an effective separation process for a wide variety of applications, especially for removal of non-biodegradable pollutants (including dyes) from wastewater [1], [2]. Adsorption capacity and characteristic of adsorbents were always examined using adsorption isotherm [3]. The linear least-squares method to the linearly transformed adsorptive equations was widely applied to confirm the experimental data and models using coefficient of determination [3], [4], [5]. However, depending on the way adsorptive equation linearized, the error distribution changes worse [6], [7], [8], [9]. So it will be an inappropriate technique to use the linearization method for estimating the adsorptive model parameters.

Adsorption isotherms of Langmuir, Freundlich, Redlich–Peterson, Koble–Corrigan and Temkin equations and pseudo-second-order model are often adopted to predict the adsorptive process in batch mode. Although linear least-square regressive analysis is often used to calculate the relative parameters [10], [11], [12], nonlinear regressive analysis is also adopted to obtain the parameters [13], [14], [15], [16]. The comparison of linear and nonlinear regressive method about these models had been analyzed [5], [6], [8].

Natural zeolite is easily obtained in many places and has been used as an adsorbent to remove dyes, ammonia ions and heavy metals [17], [18], [19]. Methylene blue (MB) is selected as a model compound in order to evaluate the capacity of natural zeolite for the removal of MB from its aqueous solutions in batch mode.

Thus, in the present study, linear and nonlinear method was used to estimate the isotherms parameters, kinetic model parameters. A comparative analysis was made between the linear and nonlinear method in estimating the relative parameters for the adsorption of MB onto zeolite. The error of prediction from two methods was analyzed.

The Langmuir adsorption isotherm has been successfully applied to many pollutants adsorption processes and has been the most widely used sorption isotherm for the sorption of a solute from a liquid solution [20]. The saturated monolayer isotherm can be represented asqe=qmKLce1+KLceThe above equation can be rearranged to the common linear form:1qe=1KLqm×1ce+1qmwhere ce is the equilibrium concentration (mg l−1); qe is the amount of MB adsorbed onto per unit mass of zeolite (mg g−1); qm is qe for a complete monolayer (mg g−1), a constant related to sorption capacity; and KL is a constant related to the affinity of the binding sites and energy of adsorption (l mg−1).

Freundlich isotherm is an empirical equation describing adsorption onto a heterogeneous surface. The Freundlich isotherm is commonly presented as [21]:qe=KFce1/nwhere KF and n are the Freundlich constants related to the adsorption capacity and adsorption intensity of the sorbent, respectively. Eq. (3) can be linearized by taking logarithms:lnqe=lnKF+1nlnce

The three-parameter Redlich–Peterson equation which has a linear dependence on concentration in the numerator and an exponential function in the denominator has been proposed to improve the fit by the Langmuir or Freundlich equation and is given by Eq. (5) [22]:qe=Ace1+Bcegwhere A, B and g are the Redlich–Peterson parameters, g lies between 0 and 1. For g = 1, Eq. (5) converts to the Langmuir form.

Three isotherm constants, A, B and g can be evaluated from the linear plot represented by Eq. (6) using a trial and error optimization method:lnAceqe1=glnce+lnB

Koble–Corrigan model is also three-parameter equation for the representing equilibrium adsorption data. It is a combination of the Langmuir and Freundlich isotherm type models and is given by Eq. (7) [23]:qe=Acen1+Bcenwhere A, B and n are the Koble–Corrigan parameters.

Three isotherm constants, A, B and n can also be evaluated from the linear plot represented by Eq. (8) using a trial and error optimization method:1qe=1Acen+BA

The derivation of the Temkin isotherm assumes that the fall in the heat of adsorption is linear rather than logarithmic, as implied in the Freundlich equation. The Temkin isotherm [24]:qe=A+Blncewhere A and B are isotherm constants.

The pseudo-second-order equation based on adsorption equilibrium capacity can be expressed as [8], [25]:dqdt=k2(qeqt)2where k2 is the rate constant of pseudo-second-order adsorption (g mg−1 min−1).

Integrating this equation for boundary conditions for t = 0, q = 0 givesqt=k2qe2t1+k2qet

The linear pseudo-second-order equation can be expressed astqt=1k2qe2+tqe

The equilibrium sorption capacity, qe, and the pseudo-second-order rate constant, k2, can be determined using linear regressive analysis by Eq. (12) or nonlinear regressive analysis by Eq. (11), respectively.

In order to confirm the fit model for the adsorption system, it is necessary to analyze the data using error analysis, combined the values of determined coefficient (R2) from regressive analysis. The calculated expressions of some error functions are as follows [9], [26], [27]:

  • (1)

    The sum of the squares of the errors (SSE):SSE=(qcqe)2

  • (2)

    The sum of the absolute errors (SAE):SAE=|(qcqe)|

  • (3)

    The average relative error (ARE):ARE=|(qcqe)/qe|n

  • (4)

    The average relative standard error (ARS):ARS=[(qcqe)/qe]2n1where n is the number of experimental data points, qc is the predicted (calculated) quantity of MB adsorbed onto zeolite according to the isotherm equations and qe is the experimental data.

Section snippets

Materials

The dye used in batch experiments was methylene blue (C.I. no. 52015). MB has a molecular weight of 373.9 g mol−1, which corresponds to methylene blue hydrochloride with three groups of water. The stock solutions of MB were prepared in distilled water (1 g l−1). All working solutions were prepared by diluting the stock solution with distilled water to the desired concentration. The values of solution pH were near 7.5.

The natural zeolite used in the present study was obtained from Xinyang city in

The effect of pH

Fig. 1 shows the effect of solution pH on MB adsorption onto zeolite at various initial solution pH for an initial dye concentration of 30 mg l−1 and zeolite dose of 6 g l−1.

From Fig. 1, the solution pH affected the values of qe. When the value of pH was from 4 to 10, the adsorption quantity was approximately constant. As the initial pH of MB solution is near 7.5, the pH of experimental solution was not adjusted.

The effect of salt concentration on adsorption

Fig. 2 shows the effect of various concentration of NaCl and CaCl2 solution on the

Conclusion

Present study showed that all the five isotherms, Langmuir, Freundlich, Redlich–Peterson, Koble–Corrigan and Temkin equation, could represent the equilibrium adsorption of MB onto natural zeolite. The kinetic process can be predicted by pseudo-second-order model. Both linear method and nonlinear method were suitable to predict the adsorption process. The Redlich–Peterson equation was best fitted to the equilibrium data from two methods. Nonlinear method was better than linear method about

Acknowledgements

The authors express their sincere gratitude to the Henan Science and Technology Department in China, for the financial support of this study. The authors also express thanks to China Postdoctoral Science Foundation (No. 20070420811) for financial support.

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